Thread Subject: SNR after matched filter?

Dear all,

I have some questions about SNR after pulse compression.

1) since noise is a random process, while signal is not, does it mean the power calculation formula is different? Noise power is calculated using average power, while signal power is calculated using total power?

noisePower = sum(noise.^2)/length(noise);
signalPower = sum(signal.^2);

2) If using matched filter to do pulse compression, how many dB in SNR increase theoretically?

3) Is matched filter just the time reversal of signal, or it need be be normalized? and how to normalized?

Anyone can give me a simple example of SNR after matched filter compared to SNR before matched filter?

Thank you very much!